$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 5x - 7$ and $ BC = 9x - 39$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {5x - 7} = {9x - 39}$ Solve for $x$ $ -4x = -32$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 5({8}) - 7$ $ BC = 9({8}) - 39$ $ AB = 40 - 7$ $ BC = 72 - 39$ $ AB = 33$ $ BC = 33$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {33} + {33}$ $ AC = 66$